The spatiotemporal evolution and memory retrieval properties of a Hopfield-like neural network with cycle-stored patterns and finite connectivity are studied. The analytical studies on a mean-field version show that, given the number of stored patterns p, there is a critical connectivity k(c) such that the retrieval states are stable Bred points if and only if k > k(c). The dependence of k(c) on the number of stored patterns is also present. The numerical simulations are applied to the short-ranged model with local interaction. It is revealed that, given p, the memory retrieval function is kept if the connectivity is high enough while the dynamics of the system is in the frozen phase. However when the connectivity k is less than a critial value k(c) the system is in the chaotic phase and loses its memory retrieval ability. The critical points of both the dynamical phase transition and memory-loss phase transition are obtained by simulation data.